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M. Cobal, PIF 2006/7
Units and kinematics
M. Cobal, PIF 2006/7
Units in particle physics
M. Cobal, PIF 2006/7
Other Units
M. Cobal, PIF 2006/7
Quantity Units HE Units SILenght 1 fm 10-15 m
Energy 1 GeV=109 eV 1.602x10-10 J
Mass 1 GeV/c2 1.78x10-27 Kg
h 6.59x10-25 GeVs 1.055x10-34 J s
c 2.998x1023 fms-1 2.998x108 ms-1
hc 0.1975 GeV fm 3.162x10-26 J m
Natural Units = c = 1Mass 1 GeVLenght 1 GeV-1
Time 1 GeV-1 1 Volt
- +
U = 1 eV
Units in particle physics
M. Cobal, PIF 2006/7
• Co-moving coordinate systems
vS S’
x x’’
Example: Muons, 2.10-6 s, in cosmic ray
p=10 GeV l v60 km (not. 600 m)
Lorentz contraction: length reduction with motion
Time dilatation: Lenght at rest
Time at rest
Lorentz transformation
M. Cobal, PIF 2006/7
Relativistic kinematics
M. Cobal, PIF 2006/7
4-vector
Invariant for rotations:
Introducing the metric:
Lorentz-invariant in terms of scalar, 4-vectors
Contro-variant 4-vecCo-variant 4-vec
Notation
M. Cobal, PIF 2006/7
Four vectors
M. Cobal, PIF 2006/7
Four vectors addition
M. Cobal, PIF 2006/7
Kinematics example
M. Cobal, PIF 2006/7
M. Cobal, PIF 2006/7
M. Cobal, PIF 2006/7
Observables
M. Cobal, PIF 2006/7
M. Cobal, PIF 2006/7
M. Cobal, PIF 2006/7
M. Cobal, PIF 2006/7
M. Cobal, PIF 2006/7
mA
mB
mC c.m. frame
Example
E
Ee
2-Body Decay
M. Cobal, PIF 2006/7
M. Cobal, PIF 2006/7
Decay Width
